In this paper, we present a transmission polarization digital holographic microscope (Pol-DHM) that allows for imaging the state of polarization of a wave front with the acquisition of a single hologram. This apparatus records, using a CCD camera, the interference in off-axis geometry between two orthogonally polarized reference waves and an object wave transmitted through a microscopic sample and magnified by a microscope objective. Since the reference waves have orthogonal polarizations, they do not interfere and the hologram results in two different fringes patterns, which can be separately filtered in the spatial Fourier domain and reconstructed separately to compute the amplitude and phase of two wave fronts. These four images allow computing the polarization ellipse azimuth and the phase difference associated with the polarization state of the object wave. The method is illustrated by imaging the strain induced in a polymethylmethacrylate (PMMA) sample and in a bended optical fiber.